Results 51 to 60 of about 1,252 (111)
New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation
International Journal of Differential Equations, Volume 2025, Issue 1, 2025.In this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=00,β≠ is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σ(t) ~ |t|−1/2 for the uniform radius of spatial analyticity of solutions to the ...
Tegegne Getachew, Jaume Giné
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Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 643-648, 1999., 1999 The generalized forced Boussinesq equation, utt − uxx + [f(u)]xx + uxxxx = h0, and its periodic traveling wave solutions are considered. Using the transform z = x − ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions.
Kenneth L. Jones, Yunkai Chen
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Forum of Mathematics, Sigma, 2015 We introduce a novel solution concept, denoted ${\it\alpha}$-dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system on the line with ...
KATRIN GRUNERT +2 more
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The equations of some dispersionless limit [PDF]
, 1995 This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations.
Son, Seung Hwan
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Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System
, 2010 In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \rho_{t}+k_{2}u\rho_{x}+(k_{1}+k_{2})\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\rho\rho_{x}=0. By the separation method,
Camassa +19 more
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.In this work, consideration is given to the initial value problem associated with the periodic fifth‐order KdV–BBM equation. It is shown that the uniform radius of spatial analyticity σ(t) of solution at time t is bounded from below by ct−2/3 (for some c > 0), given initial data η0 that is analytic on the circle and has a uniform radius of spatial ...
Tegegne Getachew, Giovanni P. Galdi
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Addendum to a paper of Craig and Goodman
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 825-827, 1994., 1994 In [1], Craig and Goodman develop the geometrical optics solution of the linearized Korteweg‐deVries equation away from caustic, or turning, points. Here we develop an analogous solution valid at caustic points.
Arthur D. Gorman
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On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation [PDF]
, 2006 Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle $\theta$ are constructed and then reduced to the two-component Camassa--Holm model.
Aratyn, H. +2 more
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.The mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems. Although the origin of nonlinear evolution equations dates back to ancient times, significant developments have been made in ...
Murat Koparan, Salim A. Messaoudi
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International Journal of Stochastic Analysis, Volume 7, Issue 1, Page 1-12, 1994., 1993 We discuss the existence, uniqueness, and continuous dependence on data, of anti‐periodic traveling wave solutions to higher order two‐dimensional equations of Korteweg‐deVries type.
Sergiu Aizicovici +2 more
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